August 7 (Wednesday)

    • 13h30 - 00h00 Registration

    • 14h20 - 14h30 Opening Ceremony

    • 14h30 - 18h00 Session 7A

      • 14h30 - 15h30 7A-1 Keynote Lecture I / slide

        • Speaker Richard P. Stanley, MIT, USA

        • Title Two enumerative tidbits

        • Abstract We discuss two unrelated results in enumerative combinatorics.

(i) Smith normal form of a matrix related to Young diagrams. We generalize a result of Carlitz, Roselle, and Scoville on a combinatorial matrix of determinant one by introducing additional parameters and computing the Smith normal form of the resulting matrix.

(ii) A distributive lattice associated with three-term arithmetic progressions (with Fu Liu). We prove two conjectures of Noam Elkies related to arithmetic progressions of length three by showing a connection with a distributive lattice of certain semistandard Young tableaux.

      • 15h45 - 16h45 7A-2 Talk I

            • Speaker Richard A. Askey, University of Wisconsin-Madison, USA

            • Title The magical connection between balanced and well-poised series, both hypergeometric and basic hypergeometric

            • Abstract Hypergeometric series with the q-binomial theorem. There are two natural first steps one can take.

(1-x)a(1-x)b = (1-x)a+b
(1-x)a(1+x)a = (1-x2)a

When the binomial theorem is used on each series and the coefficients of xn are equated, the first identity is an instance of what will become balanced series when more parameters are introduced, and the second is an instance of well-poised series, and later very well-poised series. At this stage the two identities have nothing to do with each other. At a higher level the two chains of identities become related, Whipple's formula for hypergeometric series and Watson's extension for basic hypergeometric series. Other connections will be mentioned, and two different extensions beyond this level will be described. One, which is due to George Andrews, contains variants of the Rogers-Ramanujan identities. The other has a mysterious twist which I do not understand.

      • 17h00 - 18h00 7A-3 Talk II / slide

        • Speaker Sangwook Kim, Chonnam National University, Korea

        • Title Enumeration of Schröder families by type

        • Abstract Schröder paths, sparse noncrossing partitions, and partial horizontal strips are three classes of Schröder objects which carry a notion of type. We provide type-preserving bijections among these objects and an explicit formula which enumerates these objects according to type and length. We also define a notion of connectivity for these objects and discuss an analogous formula which counts connected objects by type. This is joint work with Suhyung An and Sen-Peng Eu.